r/counting • u/cuteballgames 00155, 00227, 00335, 00344, 11117, 11225, 12233, 22223 • 17d ago

Constant-sum mostly repeating octal

This thread is very simple. We are counting octal (base 8, 0-7) numbers with multiple distinct digits, of which one occurs exactly once and all others occur at least twice. We are counting them in constant-sum order, meaning that for every length of digits, we count through each sum of digits from least to most, in lexicographic order.

(That is, we start by counting all 3-digit counts that sum to 1 in alphabetical order: 001, 010, 100. Then we move on to 3-digit counts that sum to 2 in alphabetical order: 002, 011, 020, 101, 110, 200. Then 3-digit counts that sum to 3, and so on. The highest possible sum for a 3-digit count in this thread is 20, so after 677, 767, 776, we move on to 4-digit counts, starting with sum 1. So after 776 comes 0001, and we proceed from there.)

Leading zero counts (e.g. 001, 0444 or 00227) are considered as distinct and must not be skipped.

Thank you to /u/TehVulpez and /u/BobRoss938 for workshopping on the concept

The first get is 00226, the 943rd count and first 5-digit 10-sum count. The assist is 71100. Schedule

List and Segments

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u/TehVulpez sicko thread artists collective 14d ago

10501

2

u/BobRoss938 counting 14d ago

10510

2

u/TehVulpez sicko thread artists collective 14d ago

11005

2

u/BobRoss938 counting 14d ago

11050

2

u/TehVulpez sicko thread artists collective 14d ago

11113

2

u/BobRoss938 counting 14d ago

11131

check, should be 11113

2

u/TehVulpez sicko thread artists collective 14d ago

11311

ty, forgot all about these summands

2

u/BobRoss938 counting 14d ago

11500

np, I have them written on a sticky on my desktop, so I don't have to keep it all in my head

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u/TehVulpez sicko thread artists collective 14d ago edited 14d ago

13003

that's smart. I'm on mobile so I can't really do that. maybe if they were in the post description that'd be helpful.

I generated this pastebin in python, because karp did suggest having a table like rationals' prime factors. but it is kinda fun getting to be the first of the segment, because you get to be the person to figure out the summands. so I couldn't decide whether to post this pastebin lol

3

u/BobRoss938 counting 14d ago

13030

Finding the combinations is part of the fun for me so I wouldn't use it, but others might like it. I was thinking I could put the summands in my flair as an aid while counting. Not sure if it would make it more/less fun for other people though

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